Strictly Concave Production Functions and Diminishing Average Product

Consider a production function graph where 'Total Output' is on the vertical axis and 'Labor Input' is on the horizontal axis. The function starts at the origin and curves upwards, showing that more labor leads to more output, but at a decreasing rate. Three points are marked on this curve: Point A is closest to the origin, followed by Point B, and then Point C is furthest from the origin. Based solely on a visual inspection of the rays drawn from the origin to each of these points, what can be concluded about the average product of labor?

Interpreting Production Function Geometry

Analyzing Production Efficiency

On a typical production function graph (with 'Total Output' on the vertical axis and 'Labor Input' on the horizontal axis) that exhibits diminishing average product, a point further along the curve (representing more labor) will correspond to a steeper ray from the origin compared to a point earlier on the curve.

On a production function graph with 'Total Output' on the vertical axis and 'Labor Input' on the horizontal axis, the average product of labor is represented by the slope of a ray from the origin to a point on the function. Match each graphical feature to its correct economic interpretation.

Interpreting Productivity from Production Function Geometry

On a production function graph that plots total output versus a single variable input, the average product of the input is represented by the slope of a ray from the origin to a point on the curve. If this production process exhibits diminishing average product, then as the quantity of the input increases, the slope of this ray will progressively ________.

A production function graph plots 'Total Output' on the vertical axis against 'Number of Workers' on the horizontal axis. Four points (W, X, Y, Z) are located on this production curve. The ray from the origin to Point Y is steeper than the ray to Point Z. The ray to Point W is the steepest of all four. The ray to Point X is flatter than the ray to Point W but steeper than the ray to Point Y. Arrange these points in descending order, from the one representing the highest average product of labor to the one representing the lowest.

Visualizing Worker Productivity

Evaluating Farm Productivity

Concave Production Function as the Cause of Diminishing Average Product